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Hydrodynamics: A Sea of Grains

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Transport and Fluctuations in Granular Fluids

Part of the book series: SpringerBriefs in Physics ((SpringerBriefs in Physics))

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Abstract

A granular fluid with typical boundary conditions used in laboratory or in silico, will develop structures and inhomogeneities in space and time. When spatial and temporal gradients are small, slow fields such as density, flow velocity and granular temperature evolve accordingly to the equations of granular hydrodynamics. The main steps to derive and close those equations, starting from granular Boltzmann equation, are described in this chapter. The application of the method to common situations are discussed. The interesting and still debated problem of fluctuations is introduced, in the last part of the chapter.

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References

  1. Ben-Naim, E., Chent, S.Y., Doolent, G.D., Redner, S.: Shock-like dynamics of inelastic gases. Phys. Rev. Lett. 83, 4069 (1999)

    Article  ADS  Google Scholar 

  2. Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G., Landim, C.: Macroscopic fluctuation theory. arXiv:1404.6466. (2014)

  3. Bettolo Marconi, U.M., Puglisi, A., Rondoni, L., Vulpiani, A.: Fluctuation-dissipation: response theory in statistical physics. Phys. Rep. 461, 111 (2008)

    Google Scholar 

  4. Brey, J.J., Dufty, J.W., Kim, C.S., Santos, A.: Hydrodynamics for granular flow at low density. Phys. Rev. E 58, 4638 (1998)

    Article  ADS  Google Scholar 

  5. Brey, J.J., Maynar, P., Garcia de Soria, M.I.: Fluctuating hydrodynamics for dilute granular gases. Phys. Rev. E 79:051305 (2009)

    Google Scholar 

  6. Brey, J.J., Ruiz-Montero, M.J., Moreno, F.: Steady-state representation of the homogeneous cooling state of a granular gas. Phys. Rev. E 69, 051303 (2004)

    Article  ADS  Google Scholar 

  7. Brey, J.J., Ruiz-Montero, M.J., Moreno, F.: Hydrodynamics of an open vibrated granular system. Phys. Rev. E 63, 061305 (2001)

    Google Scholar 

  8. Cencini, M., Puglisi, A., Vergni, D., Vulpiani, A., Cecconi, F (eds).: Large Deviations in Physics—Lecture Notes in Physics, volume 885. Springer, Berlin (2014)

    Google Scholar 

  9. Chapman, S., Cowling, T.G.: The Mathematical Theory of Nonuniform Gases. Cambridge University Press, London (1970)

    Google Scholar 

  10. Clerc, M.G. Argentina, M., Soto, R.: van der Waals-like transition in fluidized granular matter. Phys. Rev. Lett. 89, 044301 (2002)

    Google Scholar 

  11. Clerc, M.G., Cordero, P., Dunstan, J., Huff, K., Mujica, N., Risso, D., Varas, G.: Liquid-solid-like transition in quasi-one-dimensional driven granular media. Nat. Phys. 4, 249 (2008)

    Google Scholar 

  12. Cohen, E.G.D., Ernst, M.H.: Nonequilibrium fluctuations in space. J. Stat. Phys. 25, 153 (1981)

    Google Scholar 

  13. Costantini, G., Puglisi, A.: Fluctuating hydrodynamics in a vertically vibrated granular fluid with gravity. Phys. Rev. E 84, 031307 (2011)

    Article  ADS  Google Scholar 

  14. Deltour, P., Barrat, J.-L.: Quantitative study of a freely cooling granular medium. J. Phys. I 7, 137 (1997). France

    Google Scholar 

  15. Du, Y., Li, H., Kadanoff, L.P.: Breakdown of hydrodynamics in a one-dimensional system of inelastic particles. Phys. Rev. Lett. 74, 1268 (1995)

    Article  ADS  Google Scholar 

  16. Ferziger, J.H., Kaper, G.H.: Mathematical theory of transport processes in Gases. North-Holland, Amsterdam (1972)

    Google Scholar 

  17. Fouxon, I., Meerson, B., Assaf, M., Livne, E.: Formation and evolution of density singularities in hydrodynamics of inelastic gases. Phys. Rev. E 75, 050301(R) (2007)

    Article  ADS  Google Scholar 

  18. Garzó, V., Chamorro, M.G., Vega Reyes, F.: Transport properties for driven granular fluids in situations close to homogeneous steady states. Phys. Rev. E 87, 032201 (2013)

    Google Scholar 

  19. Goldhirsch, I.: Kinetics and dynamics of rapid granular flows. In Herrmann, H.J., Hovi, J.-P., Luding, S. (eds.) Physics of dry granular media—NATO ASI Series E 350, p. 371. Kluwer Academic Publishers, Dordrecht (1998)

    Google Scholar 

  20. Goldhirsch, I.: Scales and kinetics of granular flows. Chaos 9, 659 (1999)

    Article  ADS  MATH  Google Scholar 

  21. Goldhirsch, I., Tan, M.-L.: The single-particle distribution function for rapid granular shear flows of smooth inelastic disks. Phys. Fluids 8, 1752 (1996)

    Article  ADS  Google Scholar 

  22. Goldhirsch, I., Tan, M.-L., Zanetti, G.: A molecular dynamical study of granular fluids I: the unforced granular gas in two dimensions. J. Sci. Comput. 8, 1 (1993)

    Article  MATH  Google Scholar 

  23. Goldhirsch, I., Zanetti, G.: Clustering instability in dissipative gases. Phys. Rev. Lett. 70, 1619 (1993)

    Article  ADS  Google Scholar 

  24. Gradenigo, G., Sarracino, A., Villamaina, D., Puglisi, A.: Fluctuating hydrodynamics and correlation lengths in a driven granular fluid. J. Stat. Mech. P08017 (2011)

    Google Scholar 

  25. Gradenigo, G., Sarracino, A., Villamaina, D., Puglisi, A.: Non-equilibrium length in granular fluids: from experiment to fluctuating hydrodynamics. Europhys. Lett. 96, 14004 (2011)

    Article  ADS  Google Scholar 

  26. Haff, P.K.: Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech. 134, 401 (1983)

    Article  ADS  MATH  Google Scholar 

  27. He, X., Meerson, B., Doolen, G.: Hydrodynamics of thermal granular convection. Phys. Rev. E 65, 030301(R) (2002)

    Article  ADS  Google Scholar 

  28. Huang, K.: Statistical Mechanics. Wiley, Hoboken (1988)

    Google Scholar 

  29. Jaeger, H.M., Knight, J.B., Liu, C.-H., Nagel, S.R.: What is shaking in the sandbox? MRS Bull. XX, 25 (1994)

    Google Scholar 

  30. Jenkins, J.T., Richman, M.W.: Kinetic theory for plane shear flows of a dense gas of identical, rough, inelastic, circular disks. Phys. Fluids 28, 3485 (1985)

    Article  ADS  MATH  Google Scholar 

  31. Jenkins, J.T., Savage, S.B.: A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130, 187 (1983)

    Article  ADS  MATH  Google Scholar 

  32. Kadanoff, L.P.: Built upon sand: theoretical ideas inspired by granular flows. Rev. Mod. Phys. 71, 435 (1999)

    Article  ADS  Google Scholar 

  33. Khain, E., Meerson, B.: Onset of thermal convection in a horizontal layer of granular gas. Phys. Rev. E 67, 021306 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  34. Knight, J.B., Fandrich, C.G., Lau, C.N., Jaeger, H.M., Nagel, S.R.: Density relaxation in a vibrated granular material. Phys. Rev. E 51, 3957 (1995)

    Article  ADS  Google Scholar 

  35. Lagouge, M., Bodineau, T.: Current large deviations in a driven dissipative model. J. Stat. Phys. 139, 201 (2010)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  36. Landau, L.D., Lifchitz, E.M.: Physique Statistique. Éditions MIR (1967)

    Google Scholar 

  37. Prados, A., Lasanta, A., Hurtado, P.I.: Large fluctuations in driven dissipative media. Phys. Rev. Lett. 107, 140601 (2011)

    Google Scholar 

  38. Meerson, B., Pöschel, T., Bromberg, Y.: Close-packed floating clusters: granular hydrodynamics beyond the freezing point? Phys. Rev. Lett. 91, 024301 (2003)

    Article  ADS  Google Scholar 

  39. Meerson, B., Puglisi, A.: Towards a continuum theory of clustering in a freely cooling inelastic gas. Europhys. Lett. 70, 478 (2005)

    Article  ADS  Google Scholar 

  40. Orza, J.A.G., Brito, R., van Noije, T.P.C., Ernst, M.H.: Patterns and long range correlations in idealized granular flows. Int. J. Mod. Phys. C 8, 953 (1997)

    Article  ADS  Google Scholar 

  41. Puglisi, A., Gnoli, A., Gradenigo, G., Sarracino, A., Villamaina, D.: Structure factors in granular experiments with homogeneous fluidization. J. Chem. Phys. 136, 014704 (2012)

    Google Scholar 

  42. Puglisi, A., Loreto, V., Marconi, U.M.B., Petri, A., Vulpiani, A.: Clustering and non-gaussian behavior in granular matter. Phys. Rev. Lett. 81, 3848 (1998)

    Article  ADS  Google Scholar 

  43. Puglisi, A., Loreto, V., Marconi, U.M.B., Vulpiani, A.: A kinetic approach to granular gases. Phys. Rev. E 59, 5582 (1999)

    Article  ADS  Google Scholar 

  44. Shandarin, S.F., Zeldovich, Y.B.: The large-scale structure of the universe: turbulence, intermittency, structures in a self-gravitating medium. Rev. Mod. Phys. 61, 185 (1989)

    Google Scholar 

  45. Soto, R., Mareschal, M., Risso, D.: Departure from Fourier’s Law for Fluidized Granular Media. Phys. Rev. Lett. 83, 5003 (1999)

    Article  ADS  Google Scholar 

  46. Spohn, H.: Boltzmann Hierarchy and Boltzmann Equation, vol. 1048, p 207. Springer, Berlin (1984)

    Google Scholar 

  47. Touchette, H.: The large deviation approach to statistical mechanics. Phys. Rep. 478, 1 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  48. Trizac, E., Maynar, P., de Soria, M.I.G.: Fluctuating hydrodynamics for driven granular gases. Eur. Phys. J. 179, 123 (2009). (special topics)

    Google Scholar 

  49. van Noije, T.C.P., Ernst, M.H., Brito, R., Orza, J.A.G.: Mesoscopic theory of granular fluids. Phys. Rev. Lett. 79, 411 (1997)

    Article  ADS  Google Scholar 

  50. van Noije, T.P.C., Ernst, M.H.: Cahn-hilliard theory for unstable granular flows. Phys. Rev. E 61, 1765 (2000)

    Article  ADS  Google Scholar 

  51. van Noije, T.P.C., Ernst, M.H., Brito, R., Orza, J.A.G.: Mesoscopic theory of granular fluids. Phys. Rev. Lett. 79, 411 (1997)

    Article  ADS  Google Scholar 

  52. van Noije, T.P.C., Ernst, M.H., Trizac, E., Pagonabarraga, I.: Randomly driven granular fluids: large-scale structure. Phys. Rev. E 59, 4326 (1999)

    Article  ADS  Google Scholar 

  53. Vega Reyes, F., Santos, A., Garzó, V.: Non-newtonian granular hydrodynamics. What do the inelastic simple shear flow and the elastic fourier flow have in common? Phys. Rev. Lett. 104, 028001 (2010)

    Google Scholar 

  54. Zhou, T., Kadanoff, L.P.: Inelastic collapse of three particles. Phys. Rev. E 54, 623 (1996)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Piazzale Aldo Moro 5, I-00185, Rome, Italy

    Andrea Puglisi

  2. CNR-ISC c/o Dipartimento di Fisica, Sapienza-Università di Roma, Piazzale Aldo Moro 5, I-00185, Rome, Italy

    Andrea Puglisi

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Puglisi, A. (2015). Hydrodynamics: A Sea of Grains. In: Transport and Fluctuations in Granular Fluids. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-10286-3_3

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